Journal of Theoretical and Computational Acoustics

We consider the coupling of two-dimensional (2D) and one-dimensional (1D) models to form a single hybrid 2D–1D model for time-dependent linear wave problems. The 1D model is used to represent a 2D computational domain where the solution behaves approximately in a 1D way. This hybrid model, if designed properly, is a more efficient way to solve the full 2D model over the entire problem. Two important issues related to such hybrid 2D–1D models are (a) the design of the hybrid model and its validation (with respect to the original problem) and (b) the way the 2D–1D coupling is done, and the coupling error generated. This paper focuses on the second issue. The method used in this paper to couple the 1D and 2D models is the one proposed by Panasenko. This method has been used for mixed-dimensional coupling in many steady-state problems, and here it is being used for the first time for time-dependent problems. The hybrid formulation is derived, and the numerical accuracy and efficiency of the method are explored for a couple of basic problems.

Spurious numerical damping in the collocation boundary element method is considered for plane sound waves in two-dimensional ducts subjected to rigid and absorbing boundary conditions. Its extent is quantified in both conditions based on a damping model with exponential decay, and meshes of linear and quadratic continuous elements are studied. An exponential increase of numerical damping with respect to frequency is found and the results suggest an upper bound for given element-to-wavelength ratios. The quantification of numerical damping is required for evaluation of meshes covering a large number of waves, and real damping phenomena can be prevented from overestimation.

This work concerns the error analysis of the spectral element method with Gauss–Lobatto–Chebyshev collocation points with the implicit Newmark average acceleration scheme for the two-dimensional acoustic wave equation. The analysis is restricted to homogeneous Dirichlet boundary conditions, constant compressibility and variable density. The proposed error estimates are optimal with respect to the mesh parameter although suboptimal on the polynomial degree. Numerical examples illustrate the theoretical results.

In recent years, the boundary element method has shown to be an interesting alternative to the finite element method for modeling of viscous and thermal acoustic losses. Current implementations rely on finite-difference tangential pressure derivatives for the coupling of the fundamental equations, which can be a shortcoming of the method. This finite-difference coupling method is removed here and replaced by an extra set of tangential derivative boundary element equations. Increased stability and error reduction is demonstrated by numerical experiments.

The Bouc model describes the behavior of hysteretic materials using three-coupled differential equations. Under white noise excitation, the probability density of the state variables can be approximated using closure methods. Here, a new closure approach is presented that utilizes the beta distribution for hysteretic softening together with a nonlinear mapping using the inverse hyperbolic tangent. The beta distribution properly models the distribution of the force-proportional displacement, the required nonlinear relation between displacement, velocity, and force-proportional displacement is, however, not entirely captured for large excitation levels leading to deviations from the Monte-Carlo simulations.

We propose the nonconforming Finite Element (FE) method based on Nitsche-type mortaring for efficiently solving the inhomogeneous wave equation, where due to the change of material properties the wavelength in the subdomains strongly differs. Therewith, we gain the flexibility to choose for each subdomain an optimal grid. The proposed method fulfills the physical conditions along the nonconforming interfaces, namely the continuity of the acoustic pressure and the normal component of the acoustic particle velocity. We apply the nonconforming grid method to the computation of transmission loss (TL) of an expansion chamber utilizing micro-perforated panels (MPPs), which are modeled by a homogenization approach via a complex fluid. The results clearly demonstrate the superiority of the nonconforming FE method over the standard FE method concerning pre-processing, mesh generation flexibility and computational time.

The panel acoustic contribution analysis is used to determine the contribution of vibrating panels to the noise level inside closed spaces like a car cabin. The use of numerical techniques makes it possible to rate the panels according to their contributions accounting for the interaction between the structural vibrations and the acoustic pressure at a listening point. We consider the application of the finite and boundary element methods and the numerical Green’s function approaches to the problem and discuss the pros and cons regarding their use. The results show that the numerical Green’s function approach coupled to structure can be effectively used for the panel contribution analysis in situations with multiple panels and few listening points.

The Helmholtz equation for exterior acoustic problems can be solved by the finite element method in combination with conjugated infinite elements. Both provide frequency-independent system matrices, forming a discrete, linear system of equations. The homogenous system can be understood as a quadratic eigenvalue problem of normal modes (NMs). Knowledge about the only relevant NMs, which — when doing modal superposition — still provide a sufficiently accurate solution for the sound pressure and sound power in comparison to the full set of modes, leads to reduced computational effort. Properties of NMs and criteria of modal reduction are discussed in this work.

Sound waves in fluids are subject to viscous and thermal losses, which are particularly relevant in the so-called viscous and thermal boundary layers at the boundaries, with thicknesses in the micrometer range at audible frequencies. Small devices such as acoustic transducers or hearing aids must then be modeled with numerical methods that include losses. In recent years, versions of both the Finite Element Method (FEM) and the Boundary Element Method (BEM) including viscous and thermal losses have been developed. This paper deals with an improved formulation in three dimensions of the BEM with losses which avoids the calculation of tangential derivatives on the surface by finite differences used in a previous BEM implementation. Instead, the tangential derivatives are obtained from the element shape functions. The improved implementation is demonstrated using an oscillating sphere, where an analytical solution exists, and a condenser microphone as test cases.

We propose a nodal high-order discontinuous Galerkin (DG) method for coupled wave propagation in heterogeneous elastoplastic soil columns. We solve the elastodynamic system written in velocity-strain formulation considering simultaneously the three components of motion. A 3D Iwan elastoplastic model for dry soils under dynamic loading is introduced in the DG method (DG-3C) based on centered fluxes and a low storage Runge–Kutta time scheme. Unlike the linear case, the nonlinear material behavior results in coupling effects between different components of motion. We focus on the choice of the numerical flux for nonlinear heterogeneous media and the classical centered flux is well adapted in terms of stability and direct implementation in 3D. Several numerical applications are studied using a soil column with realistic mechanical properties, and considering successively synthetic and borehole seismic recordings recorded at the Volvi test site (northern Greece).